The initial conditions are set using the Zel'dovich Approximation.
The following were run to test this:

Cosmological model with h=0.5, Omega_m=1 and power spectrum with Gamma=0.25, n=1

The particle distribution was set up using the Zel'dovich Approximation (ZA)
 using 64^3 particles and a 64^3 grid. L is the physical distance corresponding to one grid spacing. a is the scale factor to which the evolution was done using ZA.

L= 1 Mpc         a=0.2    Power Spectrum

L= 1 Mpc         a=0.5    Power Spectrum   ZA and Linear prediction match best

L= 0.5 Mpc         a=0.2    Power Spectrum

L= 0.5 Mpc         a=0.4    Power Spectrum

L= 0.5 Mpc         a=0.5    Power Spectrum   ZA and Linear prediction match best

L= 0.5 Mpc         a=1.0    Power Spectrum

Possibly the displacements from the initial positions of the particles is not sufficient for a<0.5 and there is too much of multistreaming by the time a=1.